Which polynomial is prime?

x3 + 3x2 – 2x – 6
x3 – 2x2 + 3x – 6
4x4 + 4x3 – 2x – 2
2x4 + x3 – x + 2

  2x^4 +x^3 -x +2

Step-by-step explanation:

A polynomial is not prime if it has factors* other than itself and 1. All of the offered choices can be factored by grouping, except the last one. A graph confirms it has no real zeros.

  2x^4 +x^3 -x +2 . . . is prime

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x^3 + 3x^2 – 2x – 6 = x^2(x +3) -2(x +3) = (x^2 +2)(x +3) . . . not prime

x^3 – 2x^2 + 3x – 6 = x^2(x -2) +3(x -2) = (x^2 +3)(x -2) . . . not prime

4x^4 + 4x^3 – 2x – 2 = 2(2x^3(x +1) -(x +1)) = 2(2x^3 -1)(x +1) . . . not prime

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* Both the polynomial and the factors must have integer coefficients.

25% is the answer